Book II, Chapter XI

On the Fruitfulness of Marriages.

II.XI.1

It would be extremely desirable to be able to deduce from the registers of births, deaths and marriages in different countries, and the actual population with the rate of increase, the real prolifickness of marriages, and the true proportion of the born which lives to marry. Perhaps the problem may not be capable of an accurate solution; but we shall make some approximation towards it, and be able to account for some of the difficulties which appear in many registers, if we attend to the following considerations.

II.XI.2

It should be premised, however, that in the registers of most countries there is reason to believe that the omissions in the births and deaths are greater than in the marriages; and consequently, that the proportion of marriages is almost always given too great. In the enumerations which have lately taken place in this country, while it is supposed with reason that the registry of marriages is nearly correct, it is known with certainty that there are very great omissions in the births and deaths; and it is probable that similar omissions, though not perhaps to the same extent, prevail in other countries.

II.XI.3

If we suppose a country where the population is stationary, where there are no emigrations, immigrations, or illegitimate children, and where the registers of births deaths and marriages are accurate, and continue always in the same proportion to the population, then the proportion of the annual births to the annual marriages will express the number of children born to each marriage, including second and third marriages, and when corrected for second and third marriages, it will also express the proportion of the born which lives to marry, once or oftener; while the annual mortality will accurately express the expectation of life.

II.XI.4

But if the population be either increasing or decreasing, and the births, deaths and marriages increasing or decreasing in the same ratio, such a movement will necessarily disturb all the proportions, because the events which are contemporary in the registers are not contemporary in the order of nature, and an increase or decrease must have been taking place in the interval.

II.XI.5

In the first place, the births of any year cannot in the order of nature have come from the contemporary marriages, but must have been derived principally from the marriages of preceding years.

II.XI.6

To form a judgment then of the prolifickness of marriages taken as they occur, including second and third marriages, let us cut off a certain period of the registers of any country (30 years for instance) and inquire what is the number of births which has been produced by all the marriages included in the period cut off. It is evident, that with the marriages at the beginning of the period will be arranged a number of births proceeding from marriages not included in the period; and at the end, a number of births produced by the marriages included in the period will be found arranged with the marriages of a succeeding period. Now, if we could subtract the former number, and add the latter, we should obtain exactly all the births produced by the marriages of the period, and of course the real prolifickness of those marriages. If the population be stationary, the number of births to be added would exactly equal the number to be subtracted, and the proportion of births to marriages, as found in the registers, would exactly represent the real prolifickness of marriages. But if the population be either increasing or decreasing, the number to be added would never be equal to the number to be subtracted, and the proportion of births to marriages in the registers would never truly represent the prolifickness of marriages. In an increasing population the number to be added would evidently be greater than the number to be subtracted, and of course the proportion of births to marriages as found in the registers would always be too small to represent the true prolifickness of marriages. And the contrary effect would take place in a decreasing population. The question therefore is, what we are to add, and what to subtract, when the births and deaths are not equal.

II.XI.7

The average proportion of births to marriages in Europe is about 4 to 1. Let us suppose, for the sake of illustration, that each marriage yields four children, one every other year.*42 In this case it is evident that, wherever we begin the period in the registers, the marriages of the preceding eight years will only have produced half of their births, and the other half will be arranged with the marriages included in the period, and ought to be subtracted from them. In the same manner the marriages of the last eight years of the period will only have produced half of their births, and the other half ought to be added. But half of the births of any eight years may be considered as nearly equal to all the births of the succeeding 3¾ years. In instances of the most rapid increase it will rather exceed the births of the next 3½ years, and, in cases of slow increase, approach towards the births of the next 4 years. The mean therefore may be taken at 3¾ years.*43 Consequently, if we subtract the births of the first 3¾ years of the period, and add the births of the 3¾ years subsequent to the period, we shall have a number of births nearly equal to the births produced by all the marriages included in the period, and of course the prolifickness of these marriages. But if the population of a country be increasing regularly, and the births, deaths and marriages continue always to bear the same proportion to each other, and to the whole population, it is evident that all the births of any period will bear the same proportion to all the births of any other period of the same extent, taken a certain number of years later, as the births of any single year, or an average of five years, to the births of a single year, or an average of five years, taken the same number of years later; and the same will be true with regard to the marriages. And consequently, to estimate the prolifickness of marriages, we have only to compare the marriages of the present year, or average of five years, with the births of a subsequent year, or average of five years, taken 3¾ years later.

II.XI.8

We have supposed, in the present instance, that each marriage yields four births; but the average proportion of births to marriages in Europe is 4 to 1;*44 and as the population of Europe is known to be increasing at present, the prolifickness of marriages must be greater than 4. If, allowing for this circumstance, we take the distance of 4 years instead of 3¾ years, we may not be far from the truth. And though undoubtedly the period will differ in different countries, yet it will not differ so much as we might at first imagine; because in countries where the marriages are more prolific, the births generally follow at shorter intervals, and where they are less prolific, at longer intervals; and with different degrees of prolifickness, the length of the period might still remain the same.*45

II.XI.9

It will follow from these observations, that the more rapid is the increase of population, the more will the real prolifickness of marriages exceed the proportion of births to marriages in the registers.

II.XI.10

The rule which has been here laid down attempts to estimate the prolifickness of marriages taken as they occur; but this prolifickness should be carefully distinguished from the prolifickness of first marriages or of married women, and still more from the natural prolifickness of women in general taken at the most favourable age. It is probable, that the natural prolifickness of women is nearly the same in most parts of the world; but the prolifickness of marriages is liable to be affected by a variety of circumstances peculiar to each country, and particularly by the number of late marriages. In all countries the second and third marriages alone form a most important consideration, and materially influence the average proportions. According to Sussmilch, in all Pomerania, from 1748 to 1756 both included, the number of persons who married were 56,956, and of these 10,586 were widows and widowers.*46 According to Busching, in Prussia and Silesia, for the year 1781, out of 29,308 persons who married, 4,841, were widows and widowers,*47 and consequently the proportion of marriages will be given full one sixth too much. In estimating the prolifickness of married women, the number of illegitimate births*48 would tend, though in a slight degree, to counterbalance the overplus of marriages; and as it is found that the number of widowers who marry again, is greater than the number of widows, the whole of the correction should not on this account be applied; but in estimating the proportion of the born which lives to marry from a comparison of the marriages with the births or deaths, which is what we are now about to proceed to, the whole of this correction is always necessary.

II.XI.11

It is obvious, in the second place, that the marriages of any year can never be contemporary with the births from which they have resulted, but must always be at such a distance from them as is equal to the average age of marriage. If the population be increasing, the marriages of the present year have resulted from a smaller number of births than the births of the present year, and of course the marriages, compared with the contemporary births, will always be too few to represent the proportion of the born which lives to marry; and the contrary will take place if the population be decreasing; and, to find this proportion, we must compare the marriages of any year with the births of a previous year at the distance of the average age of marriage.

II.XI.12

But on account of the distance of this period, it may be often more convenient, though it is not essentially so correct, to compare the marriages with the contemporary deaths. The average age of marriage will almost always be much nearer to the average age of death than marriage is to birth; and consequently the annual marriages compared with the contemporary annual deaths will much more nearly represent the true proportion of the born living to marry, than the marriages compared with the births.*49 The marriages compared with the births, after a proper allowance has been made for second and third marriages, can never represent the true proportion of the born living to marry, unless when the population is absolutely stationary; but although the population be increasing or decreasing, the average age of marriage may still be equal to the average of death; and in this case the marriages in the registers compared with the contemporary deaths, (after the correction for second or third marriages, ) will nearly represent the true proportion of the born living to marry.*50 Generally, however, when an increase of population is going forwards, the average age of marriage is less than the average of death, and then the proportion of marriages, compared with the contemporary deaths, will be too great to represent the true proportion of the born living to marry; and, to find this proportion, we must compare the marriages of any particular year with the deaths of a subsequent year at such a distance from it in the registers, as is equal to the difference between the average age of marriage and the average age of death.

II.XI.13

There is no necessary connection between the average age of marriage and the average age of death. In a country, the resources of which will allow of a rapid increase of population, the expectation of life or the average age of death may be extremely high, and yet the age of marriage be very early; and the marriages then, compared with the contemporary deaths in the registers, would (even after the correction for second and third marriages) be very much too great to represent the true proportion of the born living to marry. In such a country we might suppose the average age of death to be 40, and the age of marriage only 20; and in this case, which however would be a rare one, the distance between marriage and death would be the same as between birth and marriage.

II.XI.14

If we apply these observations to registers in general, though we shall seldom be able to obtain the true proportion of the born living to marry on account of the proportions of births, deaths, and marriages not remaining the same, and of our not knowing the average age of marriage, yet we may draw many useful inferences from the information which they contain, and reconcile some apparent contradictions; and it will generally be found that, in those countries where the marriages bear a very large proportion to the deaths, we shall see reason to believe that the age of marriage is much earlier than the average age of death.

II.XI.15

In the Russian table for the year 1799, produced by Mr. Tooke, and referred to, p. 317, the proportion of marriages to deaths appeared to be as 100 to 210. When corrected for second and third marriages, by subtracting one sixth from the marriages, it will be as 100 to 252. From which it would seem to follow, that out of 252 births 200 of them had lived to marry; but we cannot conceive any country to be so healthy as that 200 out of 252 should live to marry. If however we suppose, what seems to be probable, that the age of marriage in Russia is 15 years earlier than the expectation of life or the average age of death, then, in order to find the proportion which lives to marry, we must compare the marriages of the present year with the deaths 15 years later. Supposing the births to deaths to be (as stated p. 317) 183 to 100, and the mortality 1 in 50, the yearly increase will be about 1/60 of the population; and consequently in 15 years the deaths will have increased a little above .28; and the result will be, that the marriages, compared with the deaths 15 years later will be as 100 to 322. Out of 322 births it will appear that 200 live to marry, which, from the known healthiness of children in Russia, and the early age of marriage, is a possible proportion. The proportion of marriages to births, being as 100 to 385, the prolifickness of marriages, according to the rule laid down, will be as 100 to 411; or each marriage will on an average, including second and third marriages, produce 4.11 births.

II.XI.16

The lists given in the earlier part of the chapter on Russia are probably not correct. It is suspected with reason, that there are considerable omissions both in the births and deaths, but particularly in the deaths; and consequently the proportion of marriages is given too great. There may also be a further reason for this large proportion of marriages in Russia. The Empress Catherine, in her instructions for a new code of laws, notices a custom prevalent among the peasants, of parents obliging their sons, while actually children, to marry full-grown women, in order to save the expense of buying female slaves. These women, it is said, generally become the mistresses of the father; and the custom is particularly reprobated by the Empress as prejudicial to population. This practice would naturally occasion a more than usual number of second and third marriages, and of course more than usually increase the proportion of marriages to births in the registers.

II.XI.17

In the Transactions of the Society at Philadelphia (vol. iii. No. vii. p. 25,) there is a paper by Mr. Barton, entitled Observations on the Probability of Life in the United States, in which it appears, that the proportion of marriages to births is as 1 to 4½. He mentions indeed 6½, but his numbers give only 4½. As however this proportion was taken principally from towns, it is probable that the births are given too low; and I think we may very safely take as many as five for the average of towns and country. According to the same authority the mortality is about 1 in 45; and if the population doubles every 25 years, the births would be about 1 in 20. The proportion of marriages to deaths would on these suppositions be as 1 to 2 2/9; and, corrected for second and third marriages, as 1 to 2.7 nearly. But we cannot suppose, that out of 27 births 20 should live to marry. If however the age of marriage be ten years earlier than the mean age of death, which is highly probable, we must compare the marriages of the present year with the deaths ten years later, in order to obtain the true proportion of the born which lives to marry. According to the progress of population here stated, the increase of the deaths in ten years would be a little above .3, and the result will be, that 200 out of 351, or about 20 out of 35, instead of twenty out of 27, will live to marry.*51 The marriages compared with the births 4 years later, according to the rule laid down, will in this case give 5.58 for the prolifickness of marriages. The calculations of Mr. Barton respecting the age to which half of the born live, cannot possibly be applicable to America in general. The registers, on which they are founded, are taken from Philidelphia and one or two small towns and villages, which do not appear to be so healthy as the moderate towns of Europe, and therefore can form no criterion for the country in general.

II.XI.18

In England the average proportion of marriages to births appears of late years to have been about 100 to 350. If we add 1/7 to the births instead of 1/6, which in the chapter on the Checks to Population in England, I conjectured might be nearly the amount of the omissions in the births and deaths, this will allow for the circumstance of illegitimate births; and the marriages will then be to the births as 1 to 4, to the deaths as 1 to 3.*52 Corrected for second and third marriages, the proportion of marriages to deaths will be as 1 to 3.6. Supposing the age of marriage in England about 7 years earlier than the mean age of death, the increase in these 7 years, according to the present progress of population of 1/120 yearly, would be .06, and the proportion living to marry would be 200 out of 381, or rather more than half.*53 The marriages compared with the births four years later will give 4.136 for the prolifickness of marriages.

II.XI.19

These instances will be sufficient to shew the mode of applying the rules which have been given, in order to form a judgment, from registers, of the prolifickness of marriages, and the proportion of the born which lives to marry; but it must still be remembered that they are only approximations, and intended rather to explain apparent difficulties, than to obtain results which can be depended upon as correct.

II.XI.20

It will be observed how very important the correction for second and third marriages is. Supposing each marriage to yield four births, and the births and deaths to be equal, it would at first appear necessary that, in order to produce this effect, exactly half of the born should live to marry; but if, on account of the second and third marriages, we subtract 1/6 from the marriages, and then compare them with the deaths, the proportion will be as 1 to 4 4/5; and it will appear that, instead of one half, it will only be necessary that 2 children out of 4 4/5 should live to marry. Upon the same principle, if the births were to the marriages as 4 to 1, and exactly half of the born live to marry, it might be supposed at first that the population would be stationary; but if we subtract 1/6 from the marriages; and then take the proportion of deaths to marriages as 4 to 1, we shall find that the deaths in the registers, compared with the marriages, would only be as 3 1/3 to 1; and the births would be to the deaths as 4 to 3 1/3, or 12 to 10, which is a tolerably fast rate of increase.

II.XI.21

It should be further observed, that as a much greater number of widowers marry again than of widows, if we wish to know the proportion of males which lives to marry, we must subtract full 1/5 from the marriages instead of 1/6.*54 According to this correction, if each marriage yielded 4 births, it would only be necessary that two male children out of 5 should live to marry in order to keep up the population; and if each marriage yielded 5 births, less than one third would be necessary for this purpose; and so for the other calculations. In estimating the proportion of males living to marry, some allowance ought also to be made for the greater proportion of male births.

II.XI.22

Three causes appear to operate in producing an excess of the births above the deaths: 1. the prolifickness of marriages; 2. the proportion of the born which lives to marry; and 3. the earliness of these marriages compared with the expectation of life, or the shortness of a generation by marriage and birth, compared with the passing away of a generation by death. This latter cause Dr. Price seems to have omitted to consider. For though he very justly says that the rate of increase, supposing the prolific powers the same, depends upon the encouragement to marriage, and the expectation of a child just born; yet in explaining himself, he seems to consider an increase in the expectation of life, merely as it affects the increase of the number of persons who reach maturity and marry, and not as it affects, besides, the distance between the age of marriage and the age of death. But it is evident that, if there be any principle of increase, that is, if one marriage in the present generation yields more than one in the next, including second and third marriages, the quicker these generations are repeated, compared with the passing away of a generation by death, the more rapid will be the increase.

II.XI.23

A favourable change in either of these three causes, the other two remaining the same, will clearly produce an effect upon population, and occasion a greater excess of the births above the deaths in the registers. With regard to the two first causes, though an increase in either of them will produce the same kind of effect on the proportion of births to deaths, yet their effects on the proportion of marriages to births will be in opposite directions. The greater is the prolifickness of marriages, the greater will be the proportion of births to marriages; and the greater is the number of the born which lives to be married, the less will be the proportion of births to marriages.*55 Consequently, if within certain limits, the prolificness of marriages and the number of the born living to marry increase at the same time, the proportion of births to marriages in the registers may still remain unaltered. And this is the reason why the registers of different countries, with respect to births and marriages, are often found the same under very different rates of increase.

II.XI.24

The proportion of births to marriages, indeed, forms no criterion whatever, by which to judge of the rate of increase. The population of a country may be stationary or declining with a proportion of 5 to 1, and may be increasing with some rapidity with a proportion of 4 to 1. But given the rate of increase, which may be obtained from other sources, it is clearly desirable to find in the registers a small rather than a large proportion of births to marriages; because the smaller this proportion is, the greater must be the proportion of the born which lives to marry, and of course the more healthy must be the country.

II.XI.25

Crome*56 observes that, when the marriages of a country yield less than 4 births, the population is in a very precarious state; and he estimates the prolifickness of marriages by the proportion of yearly births to marriages. If this observation were just, the population of many countries of Europe would be in a precarious state, as in many countries the proportion of births to marriages in the registers is rather below than above 4 to 1. It has been shown in what manner this proportion in the registers should be corrected, in order to make it a just representation of the prolifickness of marriages; and if a large part of the born live to marry, and the age of marriage be considerably earlier than the expectation of life, such a proportion in the registers is by no means inconsistent with a rapid increase. In Russia it has appeared that the proportion of births to marriages is less than 4 to 1; and yet its population increases faster than that of any other nation in Europe. In England the population increases more rapidly than in France; and yet in England the proportion of births to marriages, when allowance has been made for omissions, is about 4 to 1; in France 4 4/5 to 1. To occasion so rapid a progress as that which has taken place in America, it will indeed be necessary that all the causes of increase should be called into action; and if the prolifickness of marriages be very great, the proportion of births to marriages will certainly be above 4 to 1: but in all ordinary cases, where the whole power of procreation has not room to expand itself, it is surely better that the actual increase should arise from that degree of healthiness in the early stages of life which causes a great proportion of the born to live to maturity and to marry, than from a great degree of prolifickness accompanied by a great mortality. And consequently in all ordinary cases a proportion of births to marriages as 4, or less than 4, to 1 cannot be considered as an unfavourable sign.

II.XI.26

It should be observed that it does not follow that the marriages of a country are early, or that the preventive check to population does not prevail, because the greater part of the born lives to marry. In such countries as Norway and Switzerland, where half of the born live to above 40, it is evident that, though rather more than half live to marry, a large portion of the people between the ages of 20 and 40 would be living in an unmarried state, and the preventive check would appear to prevail to a great degree. In England it is probable that half of the born live to above 35;*57 and though rather more than half live to marry, the preventive check might prevail considerably (as we know it does), though not to the same extent as in Norway and Switzerland.

II.XI.27

The preventive check is perhaps best measured by the smallness of the proportion of yearly births to the whole population. The proportion of yearly marriages to the population is only a just criterion in countries similarly circumstanced, but is incorrect where there is a difference in the prolifickness of marriages or in the proportion of the population under the age of puberty, and in the rate of increase. If all the marriages of a country, be they few or many, take place young, and be consequently prolific, it is evident that, to produce the same proportion of births, a smaller proportion of marriages will be necessary; or with the same proportion of marriages a greater proportion of births will be produced. This latter case seems to be applicable to France, where both the births and deaths are greater than in Sweden, though the proportion of marriages is nearly the same, or rather less. And when, in two countries compared, one of them has a much greater part of its population under the age of puberty than the other, it is evident that any general proportion of the yearly marriages to the whole population will not imply the same operation of the preventive check among those of a marriageable age.

II.XI.28

It is, in part, the small proportion of the population under the age of puberty, as well as the influx of strangers, that occasions in towns a greater proportion of marriages than in the country, although there can be little doubt that the preventive check prevails most in towns. The converse of this will also be true; and consequently in such a country as America, where half of the population is under sixteen, the proportion of yearly marriages will not accurately express how little the preventive check really operates.

II.XI.29

But on the supposition of nearly the same natural prolifickness in the women of most countries, the smallness of the proportion of births will generally indicate, with tolerable exactness, the degree in which the preventive check prevails, whether arising principally from late, and consequently unprolific, marriages, or from a large proportion of the population above the age of puberty dying unmarried.

II.XI.30

That the reader may see at once the rate of increase, and the period of doubling, which would result from any observed proportion of births to deaths, and of these to the whole population, I subjoin two tables from Sussmilch, calculated by Euler, which I believe are very correct. The first is confined to the supposition of a mortality of 1 in 36, and therefore can only be applied to countries where such a mortality is known to take place. The other is general, depending solely upon the proportion which the excess of the births above the burials bears to the whole population, and therefore may be applied universally to all countries, whatever may be the degree of their mortality. I have now also (1825) added a third table as convenient on account of the custom of decennial enumerations in this and some other countries. It is calculated by the Rev. B. Bridge, of Peter House, Cambridge, and shows the rate of increase, or period of doubling, from the observed per-centage increase of any ten years, supposing such rate of increase to continue.

II.XI.31

It will be observed that, when the proportion between the births and burials is given, the period of doubling will be shorter, the greater the mortality; because the births as well as deaths are increased by this supposition, and they both bear a greater proportion to the whole population than if the mortality were smaller, and there were a greater number of people in advanced life.

II.XI.32

The mortality of Russia, according to Mr. Tooke, is 1 in 58, and the proportion of births 1 in 26. Allowing for the omissions in the burials, if we assume the mortality to be 1 in 52, then the births will be to the deaths as 2 to 1, and the proportion which the excess of births bears to the whole population will be 1/52.*58 According to Table II. the period of doubling will, in this case, be about 36 years. But if we were to keep the proportion of births to deaths as 2 to 1, and suppose a mortality of 1 in 36, as in Table I., the excess of births above the burials would be 1/36 of the whole population, and the period of doubling would be only 25 years.

Book II, Chapter XI, Table I.
When in any country there are 103,000 persons living, and the mortality is 1 in 36.

II.XI.33

If the proportion of deaths to births be as

Then the excess of the births will be

The proportion of the excess of the births, to the whole population, will be

And therefore the period of doubling will be

11

277

1/360

250

years.

12

555

1/180

125

13

833

1/120

83

½

14

1110

1/90

62

¾

15

1388

1/72

50

¼

16

1666

1/60

42

10:

17

1943

1/51

35

¾

18

2221

1/45

31

2/3

19

2499

1/40

28

20

2777

1/36

25

3/10

22

3332

1/30

21

1/6

25

4165

1/24

17

30

5554

1/18

12

4/5

Book II, Chapter XI, Table II.

II.XI.34

The proportion of the excess of births above the deaths to the whole of the living.

Periods of doubling in years and ten thousandth parts.

The proportion of the excess of births above the deaths to the whole of the living.

In places where there are many migrations of people, the calculations will of course be disturbed. In towns, particularly, where there is a frequent change of inhabitants, and where it often happens that the marriages of the people in the neighbouring country are celebrated, the inferences from the proportion of births to marriages are not to be depended on.

Dr. Price very justly says (Observ. on Revers. Pay. vol. i. p. 269. 4th. edit.) "that the general effect of an increase while it is going on in a country is to render the proportion of persons marrying annually, to the annual deaths greater and to the annual births less than the true proportion marrying out of any given number born. This proportion generally lies between the other two proportions, but always nearest the first." In these observations I entirely agree with him, but in a note to this passage he appears to me to fall into an error. He says, that if the prolifickness of marriages be increased (the probabilities of life and the encouragement to marriage remaining the same) both the annual births and burials would increase in proportion to the annual weddings. That the proportion of annual births would increase is certainly true; and I here acknowledge my error in differing from Dr. Price on this point in my last edition; but I still think that the proportion of burials to weddings would not necessarily increase under the circumstances here supposed.

The reason why the proportion of births to weddings increases is, that the births occurring in the order of nature considerably prior to the marriages which result from them, their increase will affect the register of births much more than the contemporary register of marriages. But the same reason by no means holds with regard to the deaths, the average age of which is generally later than the age of marriage. And in this case, after the first interval between birth and marriage, the permanent effect would be, that the register of marriages would be more affected by the increase of births than the contemporary register of deaths; and consequently the proportion of the burials to the weddings would be rather decreased than increased. From not attending to the circumstance that the average age of marriage may often be considerably earlier than the mean age of death, the general conclusion also which Dr. Price draws in this note does not appear to be strictly correct.

The reader will be aware that, as all the born must die, deaths, may in some cases be taken as synonymous with births. If we had the deaths registered of all the births which had taken place in a country during a certain period, distinguishing the married from the unmarried, it is evident that the number of those who died married, compared with the whole number of deaths, would accurately express the proportion of the births which had lived to marry.

If the proportions mentioned by Mr. Barton be just, the expectation of life in America is considerably less than in Russia, which is the reason that I have taken only ten years for the difference between the age of marriage and the age of death, instead of fifteen years, as in Russia. According to the mode adopted by Dr. Price, (vol. i. p. 272,) of estimating the expectation of life in countries the population of which is increasing, this expectation in Russia would be about 38, (births 1/26, deaths 1/50, mean 1/38), and supposing the age of marriage to be 23, the difference would be 15.

In America the expectation of life would, upon the same principles, be only 32½, (births, 1/20, deaths, 1/45, mean 1/32 ½); and supposing the age of marriage 22½, the difference would be 10.

Since this was written, I have seen reason to believe, from some calculations of Mr. Milne, actuary to the Sun Life Assurance Society, that Dr. Price's mode of estimating the expectation of life in countries that are increasing is by no means correct, and that the true expectation of life in such countries lies very much nearer the proportion of the annual mortality, than a mean between the annual mortality and the proportion of annual births; but I retain the mean proportion in the calculations of this chapter, because I find that this mean expresses more nearly the period when the deaths will equal the present births, or accord with the present marriages, than the distance of the expectation of life. In a progressive country, where the annual births considerably exceed the annual deaths, the period at which the annual deaths will equal the present annual births is less distant than the expectation of life.

Dr. Price himself has insisted strongly upon this, (vol. i. p. 270. 4th edit.) and yet he says (p. 275) that healthfulness and prolifickness are probably causes of increase seldom separated, and refers to registers of births and weddings as a proof of it. But though these causes may undoubtedly exist together, yet if Dr. Price's reasoning be just, such co-existence cannot possibly be inferred from the lists of births and weddings. Indeed the two countries, Sweden and France, to the registers of which he refers as showing the prolifickness of their marriages, are known to be by no means remarkably healthy; and the registers of towns to which be alludes, though they may show, as be intends, a want of prolifickness, yet, according, to his previous reasoning, show at the same time great healthiness, and therefore ought not to be produced as a proof of the absence of both. The general fact that Dr. Price wishes to establish may still remain true, that country situations are both more healthy and more prolific than towns: but this fact certainly cannot be inferred merely from lists of births and marriages. With regard to the different countries of Europe, it will generally be found, that those are the most healthy which are the least prolific, and those the most prolific which are the least healthy. The earlier age of marriage in unhealthy countries is the obvious reason of this fact.

The proportions here mentioned are different from those which have been taken from the additional table in Mr. Tooke's second edition; but they are assumed here as more easily and clearly illustrating the subject.
.

End of Notes

Book II, Chapter XII

Effects of Epidemics on Registers of Births, Deaths, and Marriages.

II.XII.1

It appears clearly from the very valuable tables of mortality, which Sussmilch has collected, and which include periods of 50 or 60 years, that all the countries of Europe are subject to periodical sickly seasons, which check their increase; and very few are exempt from those great and wasting plagues which, once or twice perhaps in a century, sweep off the third or fourth part of their inhabitants. The way in which these periods of mortality affect all the general proportions of births, deaths, and marriages, is strikingly illustrated in the tables for Prussia and Lithuania, from the year 1692 to the year 1757.*59

II.XII.2

The table, from which this is copied, contains the marriages, births and deaths for every particular year during the whole period; but to bring it into a smaller compass, I have retained only the general average drawn from the shorter periods of five and four years, except where the numbers for the individual years presented any fact worthy of particular observation. The year 1711, immediately succeeding the great plague, is not included by Sussmilch in any general average; but he has given the particular numbers, and if they be accurate they shew the very sudden and prodigious effect of a great mortality on the number of marriages.

II.XII.3

Sussmilch calculates that above one third of the people was destroyed by the plague; and yet, notwithstanding this great diminution of the population, it will appear by a reference to the table, that the number of marriages in the year 1711 was very nearly double the average of the six years preceding the plague.*60 To produce this effect, we may suppose that almost all who were at the age of puberty were induced, from the demand for labour and the number of vacant employments, immediately to marry. This immense number of marriages in the year could not possibly be accompanied by a great proportional number of births, because we cannot suppose that the new marriages could each yield more than one birth in the year, and the rest must come from the marriages which had continued unbroken through the plague. We cannot therefore be surprised that the proportion of births to marriages in this year should be only 2.7 to 1, or 27 to 10. But though the proportion of births to marriages could not be great; yet, on account of the extraordinary number of marriages, the absolute number of births must be great; and as the number of deaths would naturally be small, the proportion of births to deaths is prodigious, being 320 to 100; an excess of births as great, perhaps, as has ever been known in America.

II.XII.4

In the next year, 1712, the number of marriages must of course diminish exceedingly; because, nearly all who were at the age of puberty having married the year before, the marriages of this year would be supplied principally by those who had arrived at this age, subsequent to the plague. Still, however, as all who were marriageable had not probably married the year before, the number of marriages in the year 1712 is great in proportion to the population; and, though not much more than half of the number which took place during the preceding year, is greater than the average number in the last period before the plague. The proportion of births to marriages in 1712, though greater than in the preceding year, on account of the smaller comparative number of marriages, is, with reference to other countries, not great, being as 3.6 to 1, or 3.6 to 10. But the proportion of births to deaths, though less than in the preceding year, when so very large a proportion of the people married, is, with reference to other countries, still unusually great, being as 220 to 100; an excess of births, which, calculated on a mortality of 1 in 36, would double the population of a country (according to Table I. page 496) in 21 1/8 years.

II.XII.5

From this period the number of annual marriages begins to be regulated by the diminished population, and of course to sink considerably below the average number of marriages before the plague, depending principally on the number of persons rising annually to a marriageable state. In the year 1720, about nine or ten years after the plague, the number of annual marriages, either from accident, or the beginning operation of the preventive check, is the smallest; and it is at this time that the proportion of births to marriages rises very high. In the period from 1717 to 1721 the proportion, as appears by the table, is 49 to 10; and in the particular years 1719 and 1720, it is 50 to 10 and 55 to 10.

II.XII.6

Sussmilch draws the attention of his readers to the fruitfulness of marriages in Prussia after the plague, and mentions the proportion of 50 annual births to 10 annual marriages as a proof of it. There are the best reasons from the general average for supposing that the marriages in Prussia at this time were very fruitful; but certainly the proportion of this individual year, or even period, is not a sufficient proof of it, being evidently caused by a smaller number of marriages taking place in the year, and not by a greater number of births.*61 In the two years immediately succeeding the plague, when the excess of births above the deaths was so astonishing, the births bore a small proportion to the marriages; and according to the usual mode of calculation, it would have followed that each marriage yielded only 2.7 or 3.6 children. In the last period of the table, (from 1752 to 1756,) the births are to the marriages as 5 to 1, and in the individual year 1756, as 6.1 to 1: and yet during this period the births are to the deaths only as 148 to 100, which could not have been the case, if the high proportion of births to marriages had indicated a much greater number of births than usual, instead of a smaller number of marriages.

II.XII.7

The variations in the proportion of births to deaths, in the different periods of 64 years included in the table, deserve particular attention. If we were to take an average of the four years immediately succeeding the plague, the births would be to the deaths in the proportion of above 22 to 10, which, supposing the mortality to be 1 in 36, would double the population in twenty-one years. If we take the twenty years from 1711 to 1731, the average proportion of the births to deaths will appear to be about 17 to 10, a proportion which (according to Table I. page 496) would double the population in about thirty-five years. But if, instead of 20 years, we were to take the whole period of 64 years, the average proportion of births to deaths turns out to be but a little more than 12 to 10; a proportion which would not double the population in less than 125 years. If we were to include the mortality of the plague, or even of the epidemic years 1736 and 1737, in too short a period, the deaths might exceed the births, and the population would appear to be decreasing.

II.XII.8

Sussmilch thinks that, instead of 1 in 36, the mortality in Prussia, after the plague, might be 1 in 38; and it may appear perhaps to some of my readers, that the plenty occasioned by such an event ought to make a still greater difference. Dr. Short has particularly remarked that an extraordinary healthiness generally succeeds any very great mortality;*62 and I have no doubt that the observation is just, comparing similar ages together. But, under the most favourable circumstances, infants under three years are more subject to death than at other ages; and the extraordinary proportion of children which usually follows a very great mortality, counterbalances at first the natural healthiness of the period, and prevents it from making much difference in the general mortality.

II.XII.9

If we divide the population of Prussia after the plague, by the number of deaths in the year 1711, it will appear, that the mortality was nearly 1 in 31, and was therefore increased rather than diminished, owing to the prodigious number of children born in that year. But this greater mortality would certainly cease, as soon as these children began to rise into the firmer stages of life, and then probably Sussmilch's observations would be just. In general, however, we shall observe that a great previous mortality produces a more sensible effect on the births than on the deaths. By referring to the table it will appear, that the number of annual deaths regularly increases with the increasing population, and nearly keeps up the same relative proportion all the way through. But the number of annual births is not very different during the whole period, though in this time the population had more than doubled itself; and therefore the proportion of births to the whole population, at first and at last, must have changed in an extraordinary degree.

II.XII.10

It will appear therefore how liable we should be to err in assuming a given proportion of births, for the purpose of estimating the past population of any country. In the present instance, it would have led to the conclusion, that the population was scarcely diminished by the plague, although from the number of deaths it was known to be diminished one third.

II.XII.11

Variations of the same kind, though not in the same degree, appear in the proportions of births, deaths and marriages, in all the tables which Sussmilch has collected; and as writers on these subjects have been too apt to form calculations for past and future times from the proportions of a few years, it may be useful to draw the attention of the reader to a few more instances of such variations.

II.XII.12

In the Churmark of Brandenburgh,*63 during 15 years, ending with 1712, the proportion of births to deaths was nearly 17 to 10. For 6 years, ending with 1718, the proportion sunk to 13 to 10; for 4 years, ending with 1752, it was only 11 to 10; and for 4 years, ending with 1756, 12 to 10. For 3 years, ending with 1759, the deaths very greatly exceeded the births. The proportion of the births to the whole population is not given; but it is not probable that the great variations observable in the proportion of births to deaths should have arisen solely from the variations in the deaths. The proportion of births to marriages is tolerably uniform, the extremes being only 38 to 10 and 35 to 10, and the mean about 37 to 10. In this table no very great epidemics occur till the 3 years beginning with 1757, and beyond this period the lists are not continued.

II.XII.13

In the dukedom of Pomerania,*64 the average proportion of births to deaths for 60 years (from 1694 to 1756 both included) was 138 to 100; but in some of the periods of six years it was as high as 177 to 100, and 155 to 100. In others it sunk as low as 124 to 100, and 130 to 100. The extremes in the proportions of births to marriages of the different periods of 5 and 6 years, were 36 to 10 and 43 to 10, and the mean of the 60 years about 38 to 10. Epidemic years appear to have occurred occasionally, in three of which the deaths exceeded the births; but this temporary diminution of population produced no corresponding diminution of births, and the two individual years which contain the greatest proportion of marriages in the whole table occur, one in the year after, and the other two years after epidemics. The excess of deaths however was not great till the three years ending with 1759, with which the table concludes.

II.XII.14

In the Neumark of Brandenburgh,*65 for 60 years, from 1695 to 1756 both included, the average proportion of births to deaths in the first 30 years was 148 to 100, in the last 30 years 127 to 100, in the whole 60 years 136 to 100. In some periods of 5 years it was as high as 171 and 167 to 100. In others as low as 118 and 128 to 100. For 5 years ending with 1726, the yearly average of births was 7012; for 5 years ending with 1746, it was 6927, from which, judging by the births, we might infer that the population had decreased in this interval of 20 years; but it appears from the average proportion of births and deaths during this period, that it must have considerably increased, notwithstanding the intervention of some epidemic years. The proportion of births to the whole population must therefore have decidedly changed. Another interval of 20 years in the same tables gives a similar result, both with regard to the births and marriages. The extremes of the proportion of births to marriages are 34 to 10, and 42 to 10, the mean about 38 to 10. The 3 years beginning with 1757, were, as in the other tables, very fatal years.

II.XII.15

In the dukedom of Magdeburgh,*66 during 64 years ending with 1756, the average proportion of births to deaths was 123 to 100; in the first 28 years of the period 142 to 100, and in the last 34 years only 112 to 100; during one period of 5 years it was as high as 170 to 100; and in two periods the deaths exceeded the births. Slight epidemics appear to be interspersed rather thickly throughout the table. In the two instances, where three or four occur in successive years and diminish the population, they are followed by an increase of marriages and births. The extremes of the proportions of births to marriages are 42 to 10 and 34 to 10, and the mean of the 64 years 39 to 10. On this table Sussmilch remarks, that though the average number of deaths shews an increased population of one third from 1715 or 1720, yet the births and marriages would prove it to be stationary, or even declining. In drawing this conclusion however, he adds the three epidemic years ending with 1759, during which both the marriages and births seem to have diminished.

II.XII.16

In the principality of Halberstadt,*67 the average proportion of births to deaths for 68 years, ending with 1756, was 124 to 100; but in some periods of 5 years it was as high as 160 to 100, and in others as low as 110 to 100. The increase in the whole 68 years was considerable, and yet for 5 years ending with 1723, the average number of births was 2818; and for 4 years ending with 1750, 2628, from which it would appear that the population in 27 years had considerably diminished. A similar appearance occurs with regard to the marriages during a period of 32 years. In the 5 years ending with 1718, they were 727; in the 5 years ending with 1750, 689. During both these periods the proportion of deaths would have shewn a considerable increase. Epidemics seem to have occurred frequently; and in almost all the instances, in which they were such as for the deaths to exceed the births, they were immediately succeeded by a more than usual proportion of marriages, and in a few years by an increased proportion of births. The greatest number of marriages in the whole table occurs in the year 1751, after an epidemic in the year 1750, in which the deaths had exceeded the births above one third, and the four or five following years contain the largest proportion of births. The extremes of the proportions of births to marriages are 42 to 10 and 34 to 10; the mean of the 68 years 38 to 10.

II.XII.17

The remaining tables contain similar results; but these will be sufficient to shew the variations which are continually occurring in the proportions of the births and marriages, as well as of the deaths, to the whole population.

II.XII.18

It will be observed that the least variable of the proportions is that which the births and marriages bear to each other; and the obvious reason is, that this proportion is principally influenced by the prolifickness of marriages, which will not of course be subject to great changes. We can hardly indeed suppose, that the prolifickness of marriages should vary so much as the different proportions of births to marriages in the tables. Nor is it necessary that it should, as another cause will contribute to produce the same effect. The births which are contemporary with the marriages of any particular year, belong principally to marriages which had taken place some years before; and therefore, if for four or five years a large proportion of marriages were to take place; and then accidentally for one or two years a small proportion, the effect would be a large proportion of births to marriages in the registers during these one or two years; and on the contrary, if for four or five years few marriages comparatively were to take place, and then for one or two years a great number, the effect would be a small proportion of births to marriages in the registers. This was strikingly illustrated in the table for Prussia and Lithuania, and would be confirmed by an inspection of all the other tables collected by Sussmilch; in which it appears that the extreme proportions of births to marriages are generally more affected by the number of marriages than the number of births, and consequently arise more from the variations in the disposition or encouragement to matrimony, than from the variations in the prolifickness of marriages.

II.XII.19

The common epidemical years which are interspersed throughout these tables, will not of course have the same effects on the marriages and births as the great plague in the table for Prussia; but in proportion to their magnitude, their operation will in general be found to be similar. From the registers of many other countries, and particularly of towns, it appears that the visitations of the plague were frequent at the latter end of the 17th, and the beginning of the 18th centuries.

II.XII.20

In contemplating the plagues and sickly seasons which occur in these tables after a period of rapid increase, it is impossible not to be impressed with the idea, that the number of inhabitants had in these instances exceeded the food and the accommodations necessary to preserve them in health. The mass of the people would, upon this supposition, be obliged to live worse, and a greater number of them would be crowded together in one house; and these natural causes would evidently contribute to produce sickness, even though the country, absolutely considered, might not be crowded and populous. In a country even thinly inhabited, if an increase of population take place before more food is raised, and more houses are built, the inhabitants must be distressed for room and subsistence. If in the Highlands of Scotland, for the next ten or twelve years, the marriages were to be either more frequent or more prolific, and no emigration were to take place, instead of five to a cottage, there might be seven; and this, added to the necessity of worse living, would evidently have a most unfavourable effect on the health of the common people.

Book II, Chapter XII, Table IV.

II.XII.21

Annual Average.

Marriages.

Births.

Deaths.

Proportion of marriages to births.

Proportion of deaths to births.

5 yrs to 1697

5747

19715

14862

10 : 34

100 : 132

5 yrs—1702

6070

24112

14474

10 : 39

100: 165

6 yrs—1708

6082

26896

16430

10 : 44

100: 163

In 1709 &1710

a plague

number destroyed in 2 years.

247733

In 1711

12028

32522

10131

10:27

100: 320

In 1712

267

22970

10445

10 : 36

100 : 220

5 yrs to 1716

4968

21603

11984

10 : 43

100 : 180

5 yrs—1721

4324

21396

12039

10 : 49

100: 177

5 yrs-1726

4719

21452

12863

10 : 45

100: 166

5 yrs—1731

4808

29554

12825

10 : 42

100: 160

4 yrs—1735

5424

22692

15475

10 : 41

100: 146

In 1736

5280

21859

26371

Epidemic

In 1737

5765

18930

24480

years.

5 yrs to 1742

5582

22099

15255

10 : 39

100: 144

4 yrs—1746

5469

25275

15117

10 : 46

100: 167

5 yrs—1751

6423

28235

17272

10 : 43

100: 163

5 yrs—1756

5599

28892

19154

10: 50

100: 148

In the 16 yrs before the plague

95585

380516

245763

10 : 39

100 : 154

In 46 yrs after the plague

248777

1083872

690324

10 : 43

100 : 157

In 62 good yrs

344361

1464388

936087

10 : 43

100: 156

936087

More born than died

528301

In the 2 plague years

5477

23977

247733

In all the 64 years including the plague

340838

1488365

1183820

10 : 42

100 : 125

1183820

More born than died.

304545

Notes for this chapter

The number of people before the plague, according to Sussmilch's calculations, (vol. i. ch. ix. sect. 173,) was 570,000, from which if we subtract 247,733, the number dying in the plague, the remainder, 322,267, will be the population after the plague; which, divided by the number of marriages and the number of births for the year 1711, makes the marriages about one twenty-sixth part of the population, and the births about one tenth part. Such extraordinary proportions could only occur in any country in an individual year. If they were to continue, they would double the population in less than ten years. It is possible that there may be a mistake in the table, and that the births and marriages of the plague years are included in the year 1711; though as the deaths are carefully separated, it seems very strange that it should be so. It is however a matter of no great importance. The other years are sufficient to illustrate the general principle.

End of Notes

Book II, Chapter XIII

General Deductions from the preceding View of Society.

II.XIII.1

That the checks which have been mentioned are the immediate causes of the slow increase of population, and that these checks result principally from an insufficiency of subsistence, will be evident from the comparatively rapid increase which has invariably taken place, whenever, by some sudden enlargement in the means of subsistence, these checks have in any considerable degree been removed.

II.XIII.2

It has been universally remarked that all new colonies settled in healthy countries, where room and food were abundant, have constantly made a rapid progress in population. Many of the colonies from ancient Greece, in the course of one or two centuries, appear to have rivalled, and even surpassed, their mother cities. Syracuse and Agrigentum in Sicily, Tarentum and Locri in Italy, Ephesus and Miletus in Lesser Asia, were, by all accounts, at least equal to any of the cities of ancient Greece. All these colonies had established themselves in countries inhabited by savage and barbarous nations, which easily gave place to the new settlers, who had of course plenty of good land. It is calculated that the Israelites, though they increased very slowly while they were wandering in the land of Canaan, on settling in a fertile district of Egypt, doubled their numbers every fifteen years during the whole period of their stay.*68 But not to dwell on remote instances, the European settlements in America bear ample testimony to the truth of a remark, that has never I believe been doubted. Plenty of rich land to be had for little or nothing, is so powerful a cause of population, as generally to overcome all obstacles.

II.XIII.3

No settlements could easily have been worse managed than those of Spain, in Mexico, Peru, and Quito. The tyranny, superstition, and vices of the mother country were introduced in ample quantities among her children. Exorbitant taxes were exacted by the crown; the most arbitrary restrictions were imposed on their trade; and the governors were not behind hand in rapacity and extortion for themselves as well as their masters. Yet under all these difficulties, the colonies made a quick progress in population. The city of Quito, which was but a hamlet of Indians, is represented by Ulloa as containing fifty or sixty thousand inhabitants above fifty years ago.*69 Lima, which was founded since the conquest, is mentioned by the same author as equally or more populous before the fatal earthquake in 1746. Mexico is said to contain a hundred thousand inhabitants; which, notwithstanding the exaggerations of the Spanish writers, is supposed to be five times greater than what it contained in the time of Montezuma.*70

II.XIII.4

In the Portuguese colony of Brazil, governed with almost equal tyranny, there were supposed to be, above thirty years ago, six hundred thousand inhabitants of European extraction.*71

II.XIII.5

The Dutch and French colonies, though under the government of exclusive companies of merchants, still persisted in thriving under every disadvantage.*72

II.XIII.6

But the English North-American colonies, now the powerful people of the United States of America, far outstripped all the others in the progress of their population. To the quantity of rich land which they possessed in common with the Spanish and Portuguese colonies, they added a greater degree of liberty of liberty and equality. Though not without some restrictions on their foreign commerce, they were allowed the liberty of managing their own internal affairs. The political institutions which prevailed were favourable to the alienation and division of property. Lands which were not cultivated by the proprietor within a limited time, were declared grantable to any other person. In Pennsylvania there was no right of primogeniture; and in the provinces of New England, the eldest son had only a double share. There were no tithes in any of the States, and scarcely any taxes.

II.XIII.7

And on account of the extreme cheapness of good land, and a situation favourable to the exportation of grain, a capital could not be more advantageously employed than in agriculture; which, at the same time that it affords the greatest quantity of healthy work, supplies the most valuable produce to the society.

II.XIII.8

The consequence of these favourable circumstances united, was a rapidity of increase almost without parallel in history. Throughout all the northern provinces the population was found to double itself in 25 years. The original number of persons which had settled in the four provinces of New England in 1643, was 21,200. Afterwards it was calculated that more left them than went to them. In the year 1760 they were increased to half a million. They had, therefore, all along doubled their number in 25 years. In New Jersey the period of doubling appeared to be 22 years, and in Rhode Island still less. In the back settlements, where the inhabitants applied themselves solely to agriculture, and luxury was not known, they were supposed to double their number in fifteen years. Along the sea-coast, which would naturally be first inhabited, the period of doubling was about 35 years, and in some of the maritime towns the population was absolutely at a stand.*73 From the late census made in America, it appears that, taking all the States together, they have still continued to double their numbers within 25 years;*74 and as the whole population is now so great as not to be materially affected by the emigrations from Europe, and as it is known that, in some of the towns and districts near the sea-coast, the progress of population has been comparatively slow; it is evident, that in the interior of the country in general, the period of doubling from procreation only must have been considerably less than 25 years.

II.XIII.9

The population of the United States of America, according to the fourth census, in 1820, was 7,861,710. We have no reason to believe that Great Britain is less populous at present, for the emigration of the small parent stock which produced these numbers. On the contrary, a certain degree of emigration is known to be favourable to the population of the mother country. It has been particularly remarked that the two Spanish provinces, from which the greatest number of people emigrated to America, became in consequence more populous.

II.XIII.10

Whatever was the original number of British emigrants which increased so fast in North America, let us ask, Why does not an equal number produce an equal increase in the same time in Great Britain? The obvious reason to be assigned is the want of food; and that this want is the most efficient cause of the three immediate checks to population, which have been observed to prevail in all societies; is evident from the rapidity with which even old states recover the desolations of war, pestilence, famine, and the convulsions of nature. They are then for a short time placed a little in the situation of new colonies; and the effect is always answerable to what might be expected. If the industry of the inhabitants be not destroyed, subsistence will soon increase beyond the wants of the reduced numbers; and the invariable consequence will be, that population, which before perhaps was nearly stationary, will begin immediately to increase, and will continue its progress till the former population is recovered.

II.XIII.11

The fertile province of Flanders, which has been so often the seat of the most destructive wars, after a respite of a few years has always appeared as rich and populous as ever. The undiminished population of France, which has before been noticed, is an instance very strongly in point. The tables of Sussmilch afford continual proofs of a very rapid increase after great mortalities; and the table for Prussia and Lithuania, which I have inserted,*75 is particularly striking in this respect. The effects of the dreadful plague in London, in 1666, were not perceptible 15 or 20 years afterwards. It may even be doubted whether Turkey and Egypt are upon an average much less populous for the plagues which periodically lay them waste. If the number of people which they contain be considerably less now than formerly, it is rather to be attributed to the tyranny and oppression of the governments under which they groan, and the consequent discouragements to agriculture, than to the losses which they sustain by the plague. The traces of the most destructive famines in China, Indostan, Egypt, and other countries, are by all accounts very soon obliterated; and the most tremendous convulsions of nature, such as volcanic eruptions and earthquakes, if they do not happen so frequently as to drive away the inhabitants or destroy their spirit of industry, have been found to produce but a trifling effect on the average population of any state.

II.XIII.12

It has appeared from the registers of different countries, which have already been produced, that the progress of their population is checked by the periodical, though irregular, returns of plagues and sickly seasons. Dr. Short, in his curious researches into bills of mortality, often uses the expression—"terrible correctives of the redundance of mankind;"*76 and in a table of all the plagues, pestilences and famines, of which he could collect accounts, shews the constancy and universality of their operation.

II.XIII.13

The epidemical years in his table, or the years in which the plague or some great and wasting epidemic prevailed, (for smaller sickly seasons seem not to be included;) are 431,*77 of which 32 were before the Christian æra.*78 If we divide therefore the years of the present æra by 399, it will appear, that the periodical returns of such epidemics, to some countries that we are acquainted with, have been on an average only at the interval of about 4½ years.

II.XIII.14

Of the 254 great famines and dearths enumerated in the table, 15 were before the Christian æra,*79 beginning with that which occurred in Palestine, in the time of Abraham. If, subtracting these 15, we divide the years of the present æra by the remainder, it will appear that the average interval between the visits of this dreadful scourge has been only about 7½ years.

II.XIII.15

How far these "terrible correctives to the redundance of mankind" have been occasioned by the too rapid increase of population, is a point which it would be very difficult to determine with any degree of precision. The causes of most of our diseases appear to us to be so mysterious, and probably are really so various, that it would be rashness to lay too much stress on any single one; but it will not perhaps be too much to say, that among these causes we ought certainly to rank crowded houses and insufficient or unwholesome food, which are the natural consequences of an increase of population faster than the accommodations of a country with respect to habitations and food will allow.

II.XIII.16

Almost all the histories of epidemics, which we possess, tend to confirm this supposition, by describing them in general as making their principal ravages among the lower classes of people. In Dr. Short's tables this circumstance is frequently mentioned;*80 and it further appears that a very considerable proportion of the epidemic years either followed or were accompanied by seasons of dearth and bad food.*81 In other places he also mentions great plagues as diminishing particularly the numbers of the lower or servile sort of people;*82 and in speaking of different diseases he observes that those which are occasioned by bad and unwholesome food generally last the longest.*83

II.XIII.17

We know from constant experience, that fevers are generated in our jails, our manufactories, our crowded workhouses and in the narrow and close streets of our large towns; all which situations appear to be similar in their effects to squalid poverty; and we cannot doubt that causes of this kind, aggravated in degree, contributed to the production and prevalence of those great and wasting plagues formerly so common in Europe, but which now, from the mitigation of these causes, are every where considerably abated, and in many places appear to be completely extirpated.

II.XIII.18

Of the other great scourge of mankind, famine, it may be observed that it is not in the nature of things, that the increase of population should absolutely produce one. This increase, though rapid, is necessarily gradual; and as the human frame cannot be supported, even for a very short time, without food, it is evident, that no more human beings can grow up than there is provision to maintain. But though the principle of population cannot absolutely produce a famine, it prepares the way for one; and by frequently obliging the lower classes of people to subsist nearly on the smallest quantity of food that will support life, turns even a slight deficiency from the failure of the seasons into a severe dearth; and may be fairly said, therefore, to be one of the principal causes of famine. Among the signs of an approaching dearth, Dr. Short mentions one or more years of luxuriant crops together;*84 and this observation is probably just, as we know that the general effect of years of cheapness and abundance is to dispose a great number of persons to marry; and under such circumstances the return to a year merely of an average crop might produce a scarcity.

II.XIII.19

The small-pox, which may be considered as the most prevalent and fatal epidemic in Europe, is of all others, perhaps, the most difficult to account for, though the periods of its returns are in many places regular.*85 Dr. Short observes, that from the histories of this disorder it seems to have very little dependence upon the past or present constitution of the weather or seasons, and that it appears epidemically at all times and in all states of the air, though not so frequently in a hard frost. We know of no instances, I believe, of its being clearly generated under any circumstances of situation. I do not mean therefore to insinuate that poverty and crowded houses ever absolutely produced it; but I may be allowed to remark, that in those places where its returns are regular, and its ravages among children, particularly among those of the lower class, are considerable, it necessarily follows that these circumstances, in a greater degree than usual, must always precede and accompany its appearance; that is, from the time of its last visit, the average number of children will be increasing, the people will, in consequence, be growing poorer, and the houses will be more crowded till another visit removes this superabundant population.

II.XIII.20

In all these cases, how little soever force we maybe disposed to attribute to the effects of the principle of population in the actual production of disorders, we cannot avoid allowing their force as predisposing causes to the reception of contagion, and as giving very great additional force to the extensiveness and fatality of its ravages.

II.XIII.21

It is observed by Dr. Short that a severe mortal epidemic is generally succeeded by an uncommon healthiness, from the late distemper having carried off most of the declining and worn out constitutions.*86 It is probable, also, that another cause of it may be the greater plenty of room and food, and the consequently meliorated condition of the lower classes of the people. Sometimes, according to Dr. Short, a very fruitful year is followed by a very mortal and sickly one, and mortal ones often succeeded by very fruitful, as if Nature sought either to prevent or quickly repair the loss by death. In general the next year after sickly and mortal ones is prolific in proportion to the breeders left.*87

II.XIII.22

This last effect we have seen most strikingly exemplified in the table for Prussia and Lithuania.*88 And from this and other tables of Sussmilch, it also appears that, when the increasing produce of a country and the increasing demand for labour, so far meliorate the condition of the labourer as greatly to encourage marriage, the custom of early marriages is generally continued, till the population has gone beyond the increased produce, and sickly seasons appear to be the natural and necessary consequence. The continental registers exhibit many instances of rapid increase, interrupted in this manner by mortal diseases; and the inference seems to be, that those countries where subsistence is increasing sufficiently to encourage population, but not to answer all its demands, will be more subject to periodical epidemics, than those where the increase of population is more nearly accommodated to the average produce.

II.XIII.23

The converse of this will of course be true. In those countries which are subject to periodical sicknesses, the increase of population, or the excess of births above the deaths, will be greater in the intervals of these periods than is usual in countries not so much subject to these diseases. If Turkey and Egypt have been nearly stationary in their average population for the last century, in the intervals of their periodical plagues, the births must have exceeded the deaths in a much greater proportion than in such countries as France and England.

II.XIII.24

It is for these reasons that no estimates of future population or depopulation, formed from any existing rate of increase or decrease, can be depended upon. Sir William Petty calculated that in the year 1800 the city of London would contain 5,359,000*89 inhabitants, instead of which it does not now contain a fifth part of that number. Mr. Eaton has lately prophesied the extinction of the population of the Turkish empire in another century,*90 an event which will certainly fail of taking place. If America were to continue increasing at the same rate as at present for the next 150 years, her population would exceed the population of China; but though prophecies are dangerous, I will venture to say that such an increase will not take place in that time, though it may perhaps in five or six hundred years.

II.XIII.25

Europe was without doubt formerly more subject to plagues and wasting epidemics than at present; and this will account, in a great measure, for the greater proportion of births to deaths in former times, mentioned by many authors; as it has always been a common practice to estimate these proportions from too short periods, and generally to reject the years of plague as accidental.

II.XIII.26

The average proportion of births to deaths in England during the last century may be considered as about 12 to 10, or 120 to 100. The proportion in France for ten years, ending in 1780, was about 115 to 100.*91 Though these proportions undoubtedly varied at different periods during the century, yet we have reason to think that they did not vary in any very considerable degree; and it will appear therefore, that the population of France and England had accommodated itself more nearly to the average produce of each country than many other states. The operation of the preventive check—wars—the silent though certain destruction of life in large towns and manufactories—and the close habitations and insufficient food of many of the poor—prevent population from outrunning the means of subsistence; and, if I may use an expression which certainly at first appears strange, supersede the necessity of great and ravaging epidemics to destroy what is redundant. If a wasting plague were to sweep off two millions in England, and six millions in France, it cannot be doubted that, after the inhabitants had recovered from the dreadful shock, the proportion of births to deaths would rise much above the usual average in either country during the last century.

II.XIII.27

In New Jersey the proportion of births to deaths, on an average of 7 years, ending with 1743, was 300 to 100. In France and England the average proportion cannot be reckoned at more than 120 to 100. Great and astonishing as this difference is, we ought not to be so wonder-struck at it, as to attribute it to the miraculous interposition of Heaven. The causes of it are not remote, latent and mysterious, but near us, round about us, and open to the investigation of every inquiring mind. It accords with the most liberal spirit of philosophy to believe that no stone can fall, or plant rise, without the immediate agency of divine power. But we know from experience, that these operations of what we call nature have been conducted almost invariably according to fixed laws. And since the world began, the causes of population and depopulation have been probably as constant as any of the laws of nature with which we are acquainted.

II.XIII.28

The passion between the sexes has appeared in every age to be so nearly the same, that it may
always be considered, in algebraic language, as
a given quantity. The great law of necessity, which prevents population from increasing in any country beyond the food which it can either produce or acquire, is a law so open to our view, so obvious and evident to our understandings, that
we cannot for a moment doubt it. The different modes which nature takes to repress a redundant population, do not indeed appear to us so certain and regular; but though we cannot always predict the mode, we may with certainty predict the fact. If the proportion of the births to the deaths for a few years indicates an increase of numbers much beyond the proportional increased or acquired food of the country, we may be perfectly certain that, unless an emigration take place, the deaths will shortly exceed the births, and that the increase which had been observed for a few years cannot be the real average increase of the population of the country. If there were no other depopulating causes, and if the preventive check did not operate very strongly, every country would without doubt be subject to periodical plagues and famines.

II.XIII.29

The only true criterion of a real and permanent increase in the population of any country, is the increase of the means of subsistence. But even this criterion is subject to some slight variations, which however are completely open to our observation. In some countries population seems to have been forced; that is, the people have been habituated by degrees to live almost upon the smallest possible quantity of food. There must have been periods in such countries, when population increased permanently without an increase in the means of subsistence. China, India and the countries possessed by the Bedoween Arabs, as we have seen in the former part of this work, appear to answer to this description. The average produce of these countries seems to be but barely sufficient to support the lives of the inhabitants, and of course any deficiency from the badness of the seasons must be fatal. Nations in this state must necessarily be subject to famines.

II.XIII.30

In America, where the reward of labour is at present so liberal, the lower classes might retrench very considerably in a year of scarcity, without materially distressing themselves. A famine therefore seems to be almost impossible. It may be expected, that in the progress of the population of America, the labourers will in time be much less liberally rewarded. The numbers will in this case permanently increase, without a proportional increase in the means of subsistence.

II.XIII.31

In the different countries of Europe there must be some variations in the proportion of the number of inhabitants, and the quantity of food consumed, arising from the different habits of living which prevail in each state. The labourers in the south of England are so accustomed to eat fine wheaten bread, that they will suffer themselves to be half starved before they will submit to live like the Scotch peasants.

II.XIII.32

They might perhaps, in time, by the constant operation of the hard law of necessity, be reduced to live even like the lower classes of the Chinese, and the country would then with the same quantity of food support a greater population. But to effect this must always be a difficult, and every friend to humanity will hope, an abortive attempt.

II.XIII.33

I have mentioned some cases where population may permanently increase without a proportional increase in the means of subsistence. But it is evident that the variation in different states between the food and the numbers supported by it is restricted to a limit beyond which it cannot pass. In every country, the population of which is not absolutely decreasing, the food must be necessarily sufficient to support and continue the race of labourers.

II.XIII.34

Other circumstances being the same, it may be affirmed that countries are populous according to the quantity of human food which they produce or can acquire; and happy, according to the liberality with which this food is divided, or the quantity which a day's labour will purchase. Corn countries are more populous than pasture countries, and rice countries more populous than corn countries. But their happiness does not depend either upon their being thinly or fully inhabited, upon their poverty or their riches, their youth or their age; but on the proportion which the population and the food bear to each other.

II.XIII.35

This proportion is generally the most favourable in new colonies, where the knowledge and industry of an old state operate on the fertile unappropriated land of a new one. In other cases the youth or the age of a state is not, in this respect, of great importance. It is probable that the food of Great Britain is divided in more liberal shares to her inhabitants at the present period, than it was two thousand, three thousand, or four thousand years ago. And it has appeared that the poor and thinly-inhabited tracts of the Scotch Highlands are more distressed by a redundant population than the most populous parts of Europe.

II.XIII.36

If a country were never to be overrun by a people more advanced in arts, but left to its own natural progress in civilization; from the time that its produce might be considered as an unit, to the time that it might be considered as a million, during the lapse of many thousand years, there might not be a single period when the mass of the people could be said to be free from distress, either directly or indirectly, for want of food. In every state in Europe, since we have first had accounts of it, millions and millions of human existences have been repressed from this simple cause, though perhaps in some of these states an absolute famine may never have been known.

II.XIII.37

Must it not then be acknowledged by an attentive examiner of the histories of mankind, that, in every age and in every state in which man has existed or does now exist,

II.XIII.38

The increase of population is necessarily limited by the means of subsistence:

II.XIII.39

Population invariably increases when the means of subsistence increase,*92 unless prevented by powerful and obvious checks:

II.XIII.40

These checks, and the checks which keep the population down to the level of the means of subsistence, are moral restraint, vice, and misery?

II.XIII.41

In comparing the state of society which has been considered in this second book with that which formed the subject of the first, I think it appears that in modern Europe the positive checks to population prevail less, and the preventive checks more than in past times, and in the more uncivilized parts of the world.

II.XIII.42

War, the predominant check to the population of savage nations, has certainly abated, even including the late unhappy revolutionary contests; and since the prevalence of a greater degree of personal cleanliness, of better modes of clearing and building towns, and of a more equable distribution of the products of the soil from improving knowledge in political economy, plagues, violent diseases and famines have been certainly mitigated, and have become less frequent.

II.XIII.43

With regard to the preventive check to population, though it must be acknowledged that that branch of it which comes under the head of moral restraint,*93 does not at present prevail much among the male part of society; yet I am strongly disposed to believe that it prevails more than in those states which were first considered; and it can scarcely be doubted that in modern Europe a much larger proportion of women pass a considerable part of their lives in the exercise of this virtue, than in past times and among uncivilized nations. But however this may be, if we consider only the general term which implies principally a delay of the marriage union from prudential considerations, without reference to consequences, it may be considered in this light as the most powerful of the checks, which in modern Europe keep down the population to the level of the means of subsistence.

Price' s Observ. on Revers. Paym. vol. i. p. 282, 283, and vol. ii. p. 260. I have lately had an opportunity of seeing some extracts from the sermon of Dr. Styles, from which Dr. Price has taken these facts. Speaking of Rhode Island, Dr. Styles says that, though the period of doubling for the whole colony is 25 years, yet that it is different in different parts, and within land is 20 and 15 years. The population of the five towns of Gloucester, Situate, Coventry, West Greenwich and Exeter, was 5033, A. D. 1798, and 6986, A. D. 1755; which implies a period of doubling of 15 years only. He mentions afterwards, that the county of Kent doubles in 20 years, and the county of Providence in 18 years.

See an article in the Supplement to the Encyclopædia Britannica on Population, p. 308; and a curious table, p. 310, calculated by Mr. Milne, Actuary to the Sun Life Assurance Office, which strikingly confirms and illustrates the computed rate of increase in the United States, and shews that it cannot be essentially affected by immigrations.

By an increase in the means of subsistence, as the expression is used here, is always meant such an increase as the mass of the population can command; otherwise it can be of no avail in encouraging an increase of people.

End of Notes

The cuneiform inscription in the Liberty Fund logo is the earliest-known written appearance of the word "freedom" (amagi), or "liberty." It is taken from a clay document written about 2300 B.C. in the Sumerian city-state of Lagash.